If one colony held out for slavery, a dispute would have been the first thing that would have had to be sorted out after the vote. As it was, it was "kicked down the road" for resolution in the Civil War.
Are there any items today that are being "kicked down the road" for future resolution? The debt, abortion, homosexual marriage?
The story line in the musical “1776” had the SC delegation as being adamant about slavery. He tells of the hypocracy of the North in a song about the triangle trade - rum, molasses, to slaves. The trade was historically correct; I don’t know about the lead in the fight.
I believe it was both Georgia and South Carolina but the context of your story is correct.